On Mon, Mar 27, 2006 at 01:49:43PM -0500, Matt Riggsby wrote: >What I'm looking for, though, is the next step: >How can I figure out how much of that resource can be shipped to a >central point? If, say, mana pools scattered all over a region >produce x points of mana a day, which can be pumped through magical >pipelines at a cost of y points of mana per mile, how many points of >mana can be piped to a city or temple at the center of a region with a >radius of x/y miles?
If anyone else would like to check my maths, please feel free! Let's say you have a ring of radius r around your target location. There will be approximately D.r sites at that radius (assume no granularity; this is the limiting case for large radii or a high density of sites), where D is a density measure which we'll define later. Assume each site produces x resources (which I think may be a change from your symbology). The amount of resource each site can provide to the target location is x-ry (r = distance from target), so that ring as a whole produces at the target: Drx-Dr^2y If we integrate that over r (range 0 to R, the radius of the region), we get: DR^2x/2 - DR^3y/3 (total productivity less total transport costs) The total number of sites within the radius is, similarly, DR^2/2. Converting to your inputs, we can substitute: X (total production) = x D R^2/2 Total deliverable = X - X R * 2y/3x In the special case where R = x/y, then 1/3 of the produced resource is delivered. Roger _______________________________________________ GurpsNet-L mailing list <[email protected]> http://mail.sjgames.com/mailman/listinfo/gurpsnet-l
